Symbolic Math Toolbox

Deriving a Closed Form Solution for DC Motor Velocity

Introduction

We will analyze the dynamic behavior of a DC servomotor (schematic below). We will derive the system equations and derive closed form solutions for angular velocity for various input voltages.

Define System Equations

We derive the system equations by applying Kirchhoff's voltage law and Newton's 2nd Law. We know is proportional to , therefore can be expressed as. We use this relationship in defining the first equation below.

Calculate Closed Form Solution for Angular Velocity

Constant Voltage Input

We evaluate angular velocity for a constant voltage input,.

Va(s) := 1/s:omega(s) := TF*Va(s)

We convert our angular velocity expression from the frequency domain back to the time domain by taking the inverse Laplace Transform. This gives us a closed form solution for , which we plot using specified motor parameters.

As we did with the constant input, we convert the angular velocity expression to the time domain by taking the inverse Laplace Transform. We then plot angular velocity using the same motor parameters as we used previously.